Combined Approximate Message Passing for Total Variation Minimization and Randomly Translated Wavelet Denoising - Improved Compressed Sensing for Diffusion Spectrum Imaging

Jonathan I. Sperl¹, Ek T. Tan², Marion I. Menzel¹, Kedar Khare², Kevin F. King³, Christopher J. Hardy², Luca Marinelli²

Diffusion spectrum imaging (DSI) acquisition can be accelerated by randomly undersampling q-space and subsequent compressed sensing (CS) reconstruction. This work presents several extensions to CS-DSI, namely the combination of the approximate message passing (AMP) and Nesterov updates, the application of AMP to total variation minimization, and random translations for wavelet based CS. All methods can be combined yielding superior convergence properties. Fiber simulations and in vivo brain data are analyzed demonstrating the improvements in terms of speed and accuracy.